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Scaffolding in teacher-student interaction: exploring, measuring, promoting and evaluatingscaffolding

van de Pol, J.E.

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Citation for published version (APA):van de Pol, J. E. (2012). Scaffolding in teacher-student interaction: exploring, measuring, promoting andevaluating scaffolding.

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MEASURING SCAFFOLDING IN TEACHER – SMALL-GROUP INTERACTIONS

PHASE 2: MEASURING SCAFFOLDINGCHAPTER 4

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Patterns of contingent teaching in teacher-student interaction

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MEASURING SCAFFOLDING IN TEACHER – SMALL-GROUP INTERACTIONS6

AbstractThe metaphor of scaffolding has been found to be a useful and inspiring metaphor to describe the temporary and tailored support a teacher can give to a student. However, its interactive nature makes the measurement of scaffolding difficult; to our knowledge, no instrument for measuring scaffolding in classroom situations is available. In this chapter, two different instruments for analysing the scaffolding process in teacher small-group interactions are presented. We focus on what we see as the most important feature of scaffolding: its adaptive nature, or its contingency. We build on two contingency-oriented frameworks, the more qualitative and general model of contingent teaching and the more quantitative and detailed micro-level contingent shift framework. We present an analysis of 29 interaction fragments from a larger corpus of data on scaffolding. In these interaction fragments, prevocational social studies teachers support students (7th and 8th grade; 12-15 years old) performing open-ended tasks. We present detailed analyses that demonstrate that both frameworks are suitable for exploring the variability in contingency in teacher – small-group interactions. The models are complementary in that the first, general model distinguishes different phases in scaffolding interactions and emphasises the importance of the first phase (that is, diagnostic strategies), while the second, micro-level model provides detailed insight into the extent to which teachers adapt their teaching in response to student actions and the nature of these adaptations. The model of contingent teaching appears to be especially useful for practice and for teachers’ professional development. The contingent shift framework appears to be the most useful for scientific purposes.

6 This chapter is based on: Van de Pol, J., Volman, M., Elbers, E., & Beishuizen, J. (2012). Measuring scaffolding in teacher – small-group interactions. In R. Gillies (Ed.), Pedagogy: New Developments in the Learning Sciences. Hauppage: Nova Science Publishers.

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Measuring scaffolding in teacher – small-group interactions

INTRODUCTION

Although there is keen interest in small-group work (Cohen, 1994; Johnson & Johnson, 1974; Mercer & Littleton, 2007; O’Donnell, 2006), merely placing students in groups does not mean that learning will necessarily occur (Chiu, 2004; Gillies, 2006). High-quality teacher support – not only in terms of group work or collaborative learning skills but also in terms of content – is therefore vital.

Not just one particular type of support is effective in small-group work; being contingent or adaptive to students’ understanding has been pinpointed as a crucial characteristic of effective support (Chiu, 2004; Van de Pol, Volman, & Beishuizen, 2010; Webb, 2009). Contingency, or a teacher’s adaptation of his or her support to a student’s understanding, is central to the concept of scaffolding (Wood, Bruner, & Ross, 1976) which is, therefore, a powerful metaphor to describe and analyse the interaction between a learner and a more knowledgeable other. Since the introduction of this concept in 1976 by Wood et al., research on scaffolding has been ubiquitous. The concept of scaffolding has been applied and studied in many different contexts, such as parent-child interactions (Mattanah, Pratt, Cowan, & Cowan, 2005; Pino-Pasternak, Whitebread, & Tolmie, 2010), teacher-student interactions (Mercer & Fisher, 1992; Nathan & Kim, 2009), student-peer interactions (De Guerrero & Villamil, 2000), computer-student interactions (Azevedo, Cromley, Winters, Moos, & Greene, 2005), and computer-student-teacher interactions, also known as distributed scaffolding (Tabak, 2004).

Regardless of the context, scaffolding is, by nature, interactive because it always involves at least two actors (e.g., a teacher and a learner). This interactive nature makes the measurement of scaffolding difficult. Especially in naturalistic classroom situations, such as small-group work, measuring scaffolding is a challenge because teachers must work with more than one student at a time, and tasks for small-group work are often not highly structured. To our knowledge, no measurement instrument has been developed to characterise and measure scaffolding in classroom situations while taking into consideration this interactive nature (Van de Pol et al., 2010). Such an instrument, however, is needed for several reasons. First, it will enable us to compare the results of different studies in different classroom contexts. Second, it enables research, and thus understanding, of the effects of classroom scaffolding on student learning. Third, a deeper understanding of what scaffolding looks like and how it can be measured will facilitate teacher training; scaffolding can be more easily explained, taught, and assessed. Therefore, the aim of this study was to develop instruments for characterising and measuring the process of scaffolding in teacher – small-group interactions that take into account the interactive nature of scaffolding. In this chapter,

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we present the instruments we have developed, explain the usage of these instruments and, via the use of these instruments, illustrate the scaffolding process.

The Concept of Scaffolding

The metaphor of scaffolding is derived from construction work, where it represents a temporary structure that is used to construct a building. Scaffolding has been found to be a useful and inspiring metaphor for studying the temporary and tailored support a teacher can give to a student in the Zone of Proximal Development (Mercer & Littleton, 2007; Stone, 1998a; Stone, 1998b). Within Vygotsky’s sociocultural theory (1978), the Zone of Proximal Development (ZPD) represents the distance between what a student can do independently (the actual understanding) and what a student can do with the help of a more knowledgeable other (the potential understanding). The support that is given in the ZPD is often referred to as scaffolding (Mercer & Littleton, 2007).

Scaffolding can be characterised by three main features: (1) contingency, (2) fading, and (3) transfer of responsibility (Van de Pol et al., 2010). The first and most important feature is contingency, which represents the adaptive nature of the support that can be labelled as scaffolding. Not all forms of support can be called scaffolding; the support needs to be adapted to or contingent upon the students’ understanding. Fading and transfer of responsibility are closely related in that the scaffolding support should decrease over time to transfer the responsibility for the task or for learning to the student. However, fading and transfer of responsibility can only be accomplished effectively if they are performed in a contingent way. Therefore, we see contingency as the most crucial characteristic of scaffolding.

After Wood et al. introduced the concept of scaffolding in 1976, Wood, Wood, and Middleton (1978) adopted precisely this focus on contingency in their empirical study. They studied the effects of contingency on four-year-old children’s mastery of a construction task in one-to-one tutoring situations. Contingent tutoring was defined by two basic rules: when the learner fails, increase control; when the learner succeeds, decrease control7. These rules were called the contingent shift principle. All tutors’ turns were coded according to the degree of control they exerted, ranging from low control (general verbal encouragement) to high control (demonstration). Children’s turns were coded according to their understanding. In this way, every three-turn sequence of a teacher’s turn, the student’s turn and the teacher’s turn could be categorised as

7 Note that the degree of control is inherently connected to the degree to which a student is challenged; when a teacher increases control, the student is less challenged to think independently, and when a teacher decreases control, the student is more challenged to think independently.

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contingent or noncontingent. A three-sequence turn was considered contingent if the teacher increased control in reaction to an incorrect response by a student and decreased control in reaction to a correct response by a student. Contingency thus depends on the teacher’s adaptation in reaction to the student’s understanding.

Gathering information about the students’ actual understanding is crucial in contingent teaching or scaffolding. A teacher needs this information to be able to judge whether to increase or decrease the level of control. The model of contingent teaching (Van de Pol, Volman, & Beishuizen, 2011) stresses the need for gathering information about the student’s actual understanding. This model is based on the work of Wood et al. (1978) and the formative assessment literature, which promotes diagnostic strategies for contingent teaching (Ruiz-Primo & Furtak, 2007). The model of contingent teaching consists of four teaching steps (see Figure 1).

Figure 1. Model of contingent teaching

The steps of the model of contingent teaching are: (1) applying diagnostic strategies (discovering a student’s actual understanding); (2) checking one’s diagnosis with the student (summarising what the student said and asking whether this is correct to create common understanding or intersubjectivity); (3) applying intervention strategies (the actual support, adapted to the information gathered in steps 1 and 2); and (4) checking a student’s understanding (verifying whether the student learned something). Although this model focuses on the steps that a teacher can take in contingent teaching, the responses of the students are crucial to the model. A teacher needs the responses (demonstrations) of the students to determine his or her next step. Therefore, although the model adopts the teacher’s perspective in the scaffolding process, we argue that it does not neglect the interactive nature of scaffolding.

The contingent shift framework developed by Wood et al. (1976; 1978) and the model of contingent teaching both provide the means to describe and measure classroom scaffolding from an interactive perspective. Table 1 presents the characteristics of the two frameworks.

3. Intervention strategies

Student’s response

4. Checking student’s learning


1. Diagnostic strategies


2. Checking the diagnosis


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Table 1Characteristics of the Model of Contingent Teaching and the Contingent Shift Framework

Model of contingent teaching Contingent shift frameworkType Qualitative QuantitativeGranularity Macro MicroFocus Steps of contingent teaching Contingency

Unit of analysis Teacher turn Three-turn sequence of teacher turn – student turn – teacher turn

The Model of Contingent Teaching: Research

Ruiz-Primo and Furtak (2007) explored the ways in which three science teachers elicited responses from students and how the teachers used the information they gathered. They found that, in most cases, teachers elicited information about their students’ understanding; however, they did not use this information in their guidance of student learning. A case study on the ways in which three social studies teachers organised and supported small-group work (Van de Pol et al., 2011) used the model of contingent teaching to reveal patterns of contingent teaching in three of each teacher’s lessons. The separate steps of contingent teaching were identified in interaction fragments (i.e., conversations between a teacher and a small group of students), and the interaction fragments, as a whole, were considered contingent when “the teacher was judged to use information gathered about the students or students’ understanding in his provision of support to the student(s)” (p. 5). As in the study by Ruiz-Primo and Furtak (2007), contingent teaching was found to be generally scarce, partially because the support was not adapted to the students’ understanding. However, in contrast to the findings of Ruiz-Primo and Furtak (2007), Van de Pol et al. found that teachers hardly elicited information from students (e.g., through diagnostic questions). Other studies have also demonstrated teachers’ failure to adequately diagnose students’ understanding prior to instruction. Lockhorst, Wubbels, and van Oers (2010) examined the educational dialogues between two excellent biology teachers in Montessori secondary schools (preuniversity track) and small groups of students or individual students. These dialogues demonstrated that these teachers rarely employed the diagnostic language genre, in which the teacher asks information-seeking questions to explore a student’s understanding.

Elbers, Hajer, Jonkers, Koole and Prenger (2008) analysed the one-to-one interactions between two mathematics teachers and their students at two secondary schools. The results indicated that these teachers rarely explored the exact nature of the students’ problems, but instead started to give explanations right away. Therefore, diagnostic strategies (step 1 in the model of contingent teaching) were rare, and

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teachers started instruction by providing support (step 3). Chiu (2004) studied one teacher’s interventions during small-group work. The

students (9th grade) were working on algebra problems. The teacher’s evaluations of the students’ progress (i.e., diagnostic strategies) appeared to have the greatest effect on students’ subsequent time-on-task and progress in problem solving. Performing diagnostic strategies before providing students with support thus appeared to be crucial.

The model of contingent teaching appears useful for a qualitative and systematic description of the scaffolding process from a contingency perspective and, especially, for pointing out what steps teachers are and are not taking. However, these analyses are of a qualitative nature and remain rather general. Even if a teacher performs all steps in the model of contingent teaching, we cannot be sure whether the teacher is truly adapting his or her level of control to the students’ understanding. This understanding requires a micro-level analysis of the interactions between students and teachers.

The Contingent Shift Framework: Research

In parent-child studies, Wood’s contingent shift framework has been used regularly (e.g., Mattanah et al., 2005; Pino-Pasternak et al., 2010; Pratt, Green, MacVicar, & Bountrogianni, 1992). Pino-Pasternak et al. (2010) for example studied parents’ interactions with their children while helping them with their mathematics homework. The effects of authoritative parenting (i.e., “a balanced and contingent display of positive affect, responsiveness, and demandingness” p. 221) and scaffolding on the children’s performance were studied. The contingent shift framework was used to measure the degree to which parents used scaffolding; the rules of contingent teaching were applied to three-turn sequences composed of a parent’s turn, a child’s turn and a parent’s turn. The degree to which parents’ turns were contingent appeared to be a crucial and unique predictor of the child’s performance, above and beyond the effects of authoritative parenting. Pino-Pasternak et al. (2010) demonstrated that the contingent shift framework could be reliably applied to situations in which a parent helped a child on homework involving authentic and less-structured tasks. However, all of the studies mentioned here took place in one-to-one, parent-child settings; classroom settings include more diverse and complicated types of interactions.

The contingent shift framework has never been applied before in research on scaffolding in classroom settings. Our review of classroom scaffolding over the last decade has indicated that the majority of studies on scaffolding were descriptive and qualitative (Van de Pol et al., 2010). Sometimes, criteria were used to establish whether scaffolding took place. For example, Oh (2005) used the criteria developed by Maybin, Mercer, Stierer, and Norman (1992), i.e., there had to be evidence that the mentor’s

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support was contingent, that the learner accomplished the task with the mentor’s situated help, and that the learner performed the task independently (see also Mercer & Fisher, 1992). However, scaffolding has more often been described in more general terms.

When scaffolding was measured in a more quantitative way, often only the teacher’s support was taken into account. This approach does not adequately consider the interactive nature of the construct. One exception is the work of Nathan and Kim (2009). Although they did not refer to the work of Wood et al. (1976; 1978), their methodology was similar. The study examined one teacher’s regulation of conceptual reasoning and participation in mathematics whole-class interactions. The study explored not the degree of control exerted by the teacher, but rather the teacher’s adaption of the elicited cognitive complexity to the students’ understanding. The teacher tended to shift the level of cognitive complexity in response to students’ answers; he reduced the cognitive complexity in response to incorrect answers, but he increased the cognitive complexity in response to correct answers.

Although the contingent shift framework has never been applied in studies on scaffolding small-group work, the existing literature on small-group learning stresses the importance of contingency; it is the degree to which the support is contingent upon the students’ understanding and needs, as opposed to the type of support provided (e.g., specific strategies such as high vs. low content support), that is considered crucial (Chiu, 2004; Webb, 2009).

The contingent shift framework was originally intended to analyse interactions between two people; therefore, it was necessary to make some changes to adopt it to the analysis of teacher–small-group interactions. The unit of analysis consists of a teacher turn, a student turn, and a teacher turn. However, in a group of up to about five students, each student might give different responses indicating different levels of understanding. The teacher needs to react to meet the needs of each student. Therefore, the unit of analysis needs reconsideration, as well as the contingency rules on deciding upon which student(s) the teacher is being contingent.

Furthermore, in the original contingent shift framework, two types of turns (i.e., claims and demonstrations) that, in reality, do not provide the same level of information regarding the students’ actual understanding were used interchangeably. Koole (2010) distinguished between a claim of understanding (e.g., “I get it”) and a demonstration of understanding (e.g., an explanation or reason), based on Sacks (1992). A demonstration gives a teacher and a researcher much more information about a student’s understanding than a claim does; this information can be used as a tool to direct contingent instruction. If a student merely claimed not to understand a particular concept, the resulting contingent act, according to the original contingent

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shift framework, would be to increase control. However, we argue that a teacher really needs a demonstration of a student’s actual understanding to be able to take contingent action in response. Therefore, we argue that the framework requires further adaptation to address the distinction between claims and demonstrations. These issues are addressed when describing and applying the contingent shift framework.

The Current Study

In this study, we sought to develop instruments for characterising and measuring the process of scaffolding in teacher–small-group interactions, taking into account the interactive nature of scaffolding. The model of contingent teaching was used to develop an instrument for qualitative analysis of the process of scaffolding in teacher–small-group interactions. Wood’s contingent shift framework was adapted to develop a coding scheme for microanalysis of contingency in teacher–small-group interactions. The research question that is explored in this study is the following: How can classroom scaffolding in teacher–small-group interactions be analysed from a contingency perspective that takes the interactive nature of scaffolding into account?

Two research questions are formulated:1. How can the model of contingent teaching be applied to measure contingency in

teacher – small-group interactions? 2. How can the contingent shift framework be applied to measure contingency in

teacher – small group interactions?

To answer these questions, we analysed 29 interaction fragments from a larger corpus of data on scaffolding. In these interaction fragments, prevocational social studies teachers support 7th- and 8th-grade students working on open-ended tasks.

METHODS

Participants

Thirty prevocational social studies teachers, each with one 7th- or 8th-grade class, participated in this study. We recruited the teachers by placing a call for participation in several online teacher communities. Of the 30 teachers, 20 were men and 10 were women. The average teaching experience of the teachers was 9.7 years. The mean class size was 26.8 students, and the lessons lasted 53.2 minutes on average. Most

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teachers and their classes were used to working on thematic projects and in small groups. On average, 22.5 percent of the children in each class were from immigrant families (i.e., one or both parents were born abroad).

In total, 768 students participated in this study. However, because only one fragment of an interaction between each teacher and a group was selected, the total number of students for this study was 73. The average number of students within one group was 4.1, and groups ranged from 2 to 6 students. All students were between 12 and 15 years old.

Materials

Data

The data come from an experimental study with a between-subjects design and pre and postmeasurement data collection (see Van de Pol, Volman, Oort & Beishuizen, resubmitted). Thirty teachers participated in this experimental study, 17 in the scaffolding condition and 13 in the nonscaffolding condition. All teachers taught the same five-lesson curriculum on the European Union (EU). The teachers in the scaffolding condition additionally participated in a scaffolding intervention. In this intervention, teachers were trained according to the model of contingent teaching. In each session, they focused on one of the steps of contingent teaching, and in the last lesson (postmeasurement), they focused on all of the steps of contingent teaching. Each teacher’s first and last project lessons were videotaped (the premeasurement and postmeasurement sessions). During the lessons, students worked in groups. The teacher walked around, helping the groups and asking students to show their work. All interactions between a teacher and a small group of students about the subject matter were selected for analysis and are called interaction fragments. In most cases, an interaction fragment began when the teacher approached a group and ended when the teacher left. The entire corpus of data consisted of 395 interaction fragments (183 in the premeasurement session, 212 in the postmeasurement session) in which a teacher provided support to a small group of students regarding the subject matter. One interaction fragment in each teacher’s last lesson (i.e., postmeasurement) was randomly selected for the analyses in this chapter. We selected only interaction fragments from the postmeasurement because we expected to find more variability in contingency in these fragments. In the postmeasurement, the teachers in the scaffolding condition had already participated in the scaffolding intervention, whereas the teachers in the nonscaffolding condition had not. In every class, an audio recorder was placed on the desk of a randomly chosen group during the entire lesson. If possible, an interaction between a teacher and this

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group was chosen so that we could compare how the group worked before and after the arrival of the teacher. However, this condition was not met for 12 of the teachers; in these cases, an interaction fragment between the teacher and another group was randomly selected. For these groups, we therefore only had the video fragments of their interactions with the teacher; no audio of the group work before the arrival or after the departure of the teacher was available. The recordings of one teacher in the nonscaffolding condition were not usable; therefore, we were left with a total of 29 interaction fragments with a total duration of 41 minutes.

From these 29 interaction fragments, three fragments were chosen as typical fragments. The first fragment is considered a typical nonscaffolding example without any diagnostic strategies (step 1), the second fragment is considered a typical nonscaffolding example with diagnostic strategies, and the third fragment is considered a typical scaffolding example. The fragments were first selected by the first author at face value and thereafter were shared and discussed with the other authors to decide whether these fragments could be considered exemplary cases.

Lesson content

All students completed a five-lesson project on the EU. Each student had an individual workbook that contained all the necessary information. The work booklet also contained explanations of the assignments and informative texts as well as a list explaining all of the relevant concepts. Each group also had a group booklet, in which they wrote out their actual assignments. The example transcripts were derived from the last of the five project lessons. In the last lesson, the students worked on an assignment called “Which Word Out” (Leat, 1998). This assignment consisted of four steps: (1) check whether you understand all of the concepts on the given list of concepts; (2) choose two series of three related concepts; (3) choose one concept per series that could be omitted; and (4) give two reasons for your choice.

The model of contingent teaching

The model of contingent teaching consists of four steps: (1) diagnostic strategies, (2) checking the diagnosis, (3) intervention strategies, and (4) checking students’ learning (see Figure 1). We developed a coding system for scoring turns by teachers. We use the term turn to indicate a complete utterance by a student or a teacher before another student or teacher says something. We coded a turn as step 1 (diagnostic strategy) when the teacher used it “to discover the level of the student’s ability to perform the task without assistance” (Tharp & Gallimore, 1988, p. 59). We defined

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step 2 (checking the diagnosis) as a teacher’s verification of whether he or she has understood the student correctly and coded turns according to this definition. We coded a turn as intervention strategy (step 3) when it contained a strategy used to support the student8. A step 4 turn was one in which the teacher attempted to discover a student’s understanding of a concept about which he or she had already received assistance.

In our previous research, we used this model as a basis for guiding the professional development of teachers (Van de Pol, Volman, Beishuizen, 2012). In this previous study, we used an additional criterion to determine the contingency of an interaction fragment as a whole:

We considered an interaction fragment to be contingent when we judged the teacher to support the students with exactly that which was not grasped by the students. An implicit prerequisite for contingency was that information about the students’ current understanding be explicitly gathered by the teacher if not spontaneously offered by the student(s) (Van de Pol et al. 2012, p. 197).

We used Krippendorff’s Alpha (Krippendorff, 2004) to express the interrater reliability. The commonly used Cohen’s Kappa (1960) often results in inaccurately high values if the frequency distributions of two raters differ to a great extent (Krippendorff, 2004: Strijbos & Stahl, 2007). Approximately 10% of the data (20 interaction fragments out of the total of 212 in the postmeasurement phase) was coded independently by two coders with regard to the separate steps of contingent teaching, with a Krippendorff’s Alpha of .73. The interrater reliability of the contingent teaching steps was considered satisfactory because Krippendorff (2004) states that values between .67 and .80 still enable cautious conclusions.

When 10% of the data was coded by two observers, it was determined that the coding of contingency, according to the additional rule in the interaction fragments, was reliable. The agreement was substantial, with a Krippendorff’s Alpha of .88.

The contingent shift framework

Following the methodology of Wood et al. (1978), we developed a contingent shift framework for the purpose of measuring contingency in classroom interactions between a teacher and a small group of students. As contingency involves adapting the level of

8 We acknowledge that students’ responses to the intervention strategies give the teacher information about a students’ understanding, and this also constitutes a diagnostic strategy. However, a turn was only coded as a diagnostic strategy (step 1) if it was only diagnosing the students’ understanding and was not giving support.

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control that is exerted in support of student understanding, it was precisely these two variables that needed to be measured first. In addition, we measured the students’ mode of expression (claim versus demonstration). Thereafter, we were able to apply contingency rules based on the contingent shift principle of Wood et al. (1978). The degree of teacher control, student understanding and student’s mode of expression were coded at the turn level.

Teacher’s degree of control

The teachers’ turns were coded according to the degree of control maintained by the teacher. Code values ranged from no control (0) to a high level of control (5). If a turn did not deal with the lesson content (e.g., how a task is performed), it was coded as “teacher not on content” (TDcNOC) (see Table 2).

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Table 2Degree of Teacher Control Teacher degree of control (TDc)

Description Example

Teacher not on content (TDcNOC)

What the teacher says is unrelated to the subject matter

This lesson ends in five minutesYou can’t go to the bathroom now

0. No control (TDc0) The teacher is not with the group

Before the teacher arrives at the groupAfter the interaction, when the teacher walks away

1. Lowest (TDc1)

The teacher:- Provides no new content - Elicits an elaborate response- Asks a broad and open question

Why did your group choose those three concepts? What are the similarities between those three concepts? What have you written down?

2. Low (TDc2)

The teacher:- Provides no new content - Elicits an elaborate response, mostly for an elaboration or explanation of something (“why” questions)- Asks a more detailed but still open question

What do you think “prosperity” means? S: The Polish people came hereT: Why do you think they came here?

3. Medium (TDc3)

The teacher:- Provides no new content - Elicits a short response

Yes/no or multiple choice questionsFeedback; the teacher indicates that something is not right, but doesn’t indicate what it should be

4. High (TDc4)

The teacher:- Provides new content - Elicits a response- Gives a hint or suggestive question

Have you thought about the internal market? [when this concept had not been mentioned yet]Think about [new concept]

5. Highest (TDc5)

The teacher:- Provides new content - Elicits no response- Gives an explanation or the answer to a question

The answer is “prosperity”Well, prosperity is about making money, and rights indicate, for example, the rights you have that must be respected.

Students’ understanding

All student turns were categorised according to a five-level scale (cf. Pino-Pasternak et al. (2010) (see Table 3). Student understanding was coded according to the apparent judgment of the teacher in the interaction fragment. In other words, when a teacher approved of a student’s answer, the answer was considered correct, but when a teacher disapproved or asked a follow-up question, the answer was, in turn, coded as poor understanding or partial understanding. We chose this method because we wanted to measure the contingency of the teacher’s approach to the student. The teacher decides, based upon his or her assessment of the students’ understanding, the level of control that he/she will assert. Therefore, the use of a more objective criterion (e.g., based on the subject matter itself) could potentially result in conflicting decisions; we might judge a three-turn sequence to be noncontingent while the teacher

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is, according to his or her own judgement, being contingent. Therefore, we chose to adopt the teacher’s perspective regarding contingency.

Table 3Levels of Student UnderstandingLevel of student understanding (SU) DescriptionLevel 0 (SU0) Poor or no understandingLevel 1 (SU1) Partial understandingLevel 2 (SU2) Good understanding

Level X (SUX) No understanding can be determined, but the turn is about the content

Not on content (SUNOC) Student turn about, for example, organisational matters

Student modes of expression

All student turns were also coded according to their mode of expression. We distinguished between claims, minimal demonstrations and extensive demonstrations (see Table 4).

Table 4Categories of Student Mode of Expression

Student Mode (SM) ExamplesNot on content (SMNOC) - Can I go to the toilet?

0. Claim (SM0)- I don’t get this- Aha!- T: Do you get it? S: Yes

1. Demonstration minimal (SM1) - T: To what category does this article belong? S: To peace

2. Demonstration extensive (SM2)- T: Why are these three concepts related? S: Because they are all about money and economics and how people trade in the EU.

Contingency rules

In principle, we followed the contingency rules of Wood et al. (1978). Increasing the level of control after a student’s demonstration of poor understanding and decreasing the level of control after a student’s demonstration of good understanding was considered contingent. When a student demonstrated partial understanding, staying at the same level of control or increasing the level of control was considered contingent. It is important to note that we only used student’s demonstrations to

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determine contingency. If a student only claimed a particular level of understanding, eliciting demonstrations was considered contingent (the specific rules governing claims and other exceptions can be found in Appendix H). The contingency rules for student demonstrations are provided in Table 5.

Table 5Contingency Rules for Students’ Demonstrations

Three-turn-sequence* Contingency

Teacher turn 1 Student turn – demonstration Teacher turn 2

First three-turn sequence

TDc0 (teacher not yet there)

SU0TDc1 or TDc2

ContingentSU1 ContingentSU2 Not contingent

Middle three-turn sequences

TDc1 to TDc4SU0

More in control than in turn 1

ContingentSU1 ContingentSU2 Not contingent

TDc2 to TDc5SU0

Less in control than in turn 1

Not contingentSU1 Not contingentSU2 Contingent

TDc2 – TDc4SU0

Same level of control as in turn 1

Not contingentSU1 ContingentSU2 Not contingent

TDc5SU0

TDc5Contingent

SU1 ContingentSU2 Not contingent

TDc1SU0

TDc1Not contingent

SU1 ContingentSU2 Contingent

Last three-turn sequence TDc1 to TDc4

SU0 TDc0 (teacher walks away) or TDc1 (lowest level control)

Not contingentSU1 Not contingentSU2 Contingent

Note. Teacher’s degree of control (TDc): TDc0=no control; TDc1=lowest control, TDc2=low control, TDc3=medium control, TDc4=high control, TDc5=highest control. Student understanding (SU): SU0=poor understanding, SU1=partial understanding, SU2=good understanding*A three-turn-sequence consists of three subsequent turns: teacher turn – student turn – teacher turn.

In principle, the unit of analysis consisted of a three-turn sequence (a teacher’s turn, a student’s turn, and the next teacher’s turn). If, for example, two student turns occurred between the two teacher turns, we broke the interaction down into two three-turn sequences, each including only one of the student turns. If an off-subject turn occurred within a three-turn sequence, this turn was ignored and had no influence upon

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the analyses.The first three-turn sequence in an interaction fragment (Table 5) refers to the first

triad of a teacher turn, a student turn and a teacher turn that occurs in an interaction fragment. If the interaction fragment is initiated by the student, the first teacher turn is always coded as no control because the teacher is initially not present to interact with the group. If the student’s turn (i.e., a demonstration) is coded as poor understanding (SU0) or partial understanding (SU1) and the teacher’s level of control increases, the three-turn sequence is coded as contingent. If the student’s demonstration is, however, coded as good understanding (SU2) and the teachers’ level of control increases, the three-turn sequence is coded as not contingent because the teacher is helping even though this is not necessary.

Three scenarios are possible for the middle three-turn sequences of an interaction fragment (Table 5). First, the teacher’s degree of control increases. This is only considered contingent if the student’s demonstration was coded as poor understanding (SU0) or partial understanding (SU1). Second, the teacher’s degree of control decreases. This behaviour is only considered contingent if the student’s demonstration was coded as good understanding (SU2). Third, the teacher’s degree of control stays the same. In this case, there are several options. For the middle levels of control (TDc1 to TDc4), staying at the same level is only coded as contingent when the student’s demonstration was coded as partial understanding (SU2). For the highest level of control (TDc5), staying at the same level of control is contingent when the student’s demonstration was coded as poor understanding (SU0) or partial understanding (SU1). For the lowest level of control (TDc1), staying at the same level is only contingent when the student’s demonstration was coded as good understanding (SU2).

As for the last three-turn sequence in an interaction fragment (Table 5), exerting no control (TDc0=walking away from the group) is only contingent if the student had demonstrated good understanding (SU2).

In the analyses using the contingent shift framework, we were also able to determine whether the teacher was being contingent towards one student in particular or towards the group as a whole. If two succeeding three-turn sequences involve one and the same student, we can say that the teacher has adapted his or her level of control to the understanding of that particular student. If, however, two succeeding three-turn sequences involve different students, we cannot say that the teacher is adapting his or her support to the understanding of one particular student and can thus infer that he or she is considering the levels of other students or of the entire group.

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Reliability

Ten percent of the data (26 interaction fragments out of the total of 212 in the postmeasurement) was coded by two coders to establish the interrater reliability for the variable of teacher’s degree of control. We calculated a Krippendorff’s Alpha of .85. We considered the interrater reliability substantial because Krippendorff (2004) states that values of .80 and above represent a high level of agreement.

About five percent of the data (10 interaction fragments out of the total of 212 in the postmeasurement) was coded by two coders to establish the interrater reliability for the variable of student’s understanding. We calculated a Krippendorff’s Alpha of .75. We considered the interrater reliability substantial.

About five percent of the data (12 interaction fragments out of the total of 212 in the postmeasurement) was coded by two coders to establish the interrater reliability for the variable of student mode of expression. We calculated a Krippendorff’s Alpha of .71 and considered the interrater reliability substantial.

To calculate the intrarater reliability, the first author coded almost ten percent of the data (17 interaction fragments) twice with an interval of four months. The intrarater reliability appeared to be high: Krippendorff’s Alpha was .87 for teacher’s degree of control, .95 for students’ understanding, .and .88 for student mode of expression.

RESULTS

In this section, we will first qualitatively characterise the scaffolding process by applying the model of contingent teaching to the three example fragments to explore research question 1 (How can the model of contingent teaching be applied to measure contingency in teacher – small-group interactions?). Then we will present quantitative analyses of the entire data set, including the three example fragments, to explore research question 2 (How can the contingent shift framework be applied to measure contingency in teacher – small group interactions?).

Characterising Scaffolding with the Model of Contingent Teaching

Here, we will use the model of contingent teaching to characterise the process of scaffolding in teacher – small-group interactions in three example interaction fragments. It is important to note that, for now, we are not addressing the issue of the teacher’s contingency towards particular students. For now, the group of students is, so to speak, seen as a single entity.

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Example fragment, Patricia: Nonscaffolding without diagnostic strategies

In the lesson from which the first example fragment stems, the teacher (Patricia) walked around the classroom and monitored the groups’

progress. The group of four students that was supported in this example fragment had been working for about five minutes on the assignment before the teacher arrived. The students had been working seriously and came up with multiple series of three concepts that they thought were related to each other. They also stated that they found the assignment difficult. As the teacher walked by, one student (student 3) attracted the teacher’s attention. This student had found two related concepts, but did not know which third concept related to the two he had selected. The example interaction fragment is provided below. Note that, for the purpose of readability, punctuation has been added to the transcript. Crucial (nonverbal) information is added in parentheses.

Example fragment, Patricia1 Teacher (not there yet)2 Student 3 Miss, look, “when it’s up to one person” and, here, “more citizens”

3 TeacherYes, so you need one more concept. You already have two concepts, democracy and dictatorship. Which one could go with these? Because these do not go together, in the end you have to find one more concept that fits with one of yours. For example,this one (points in the booklet) [step 3: intervention strategy]

4 Student 3 “Human rights?” (reads from the booklet)

5 Teacher Yes, and does that go with dictatorship or with, eh, democracy? [step 3: intervention strategy]

6 Student 3 Eh, democracy

7 Teacher Yes, so now you have three concepts and one does not belong (walks away) [step3: intervention strategy]

After the teacher had left, the students started to work with the series of democracy, dictatorship and human rights, as proposed by the teacher. However, they could not come up with a good reason why they should omit one concept. They did not seem to understand why these three concepts went together in the first place. After a while, they became frustrated.

If we approach this interaction fragment using the model of contingent teaching, we see that the teacher is only performing intervention strategies (step 3 in the model of contingent teaching). We (and the teacher) have no idea of the students’ understanding. What does the student already know and what exactly is he or she struggling with? Perhaps the student had already considered a third concept but was not sure whether it went with the other two. This example is typical of nonscaffolding interactions. The additional criterion for establishing contingency in interaction fragments states that the

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teacher needs to help students with exactly those concepts that they do not understand; this requires the teacher to gather information about the students’ current levels of understanding. When we apply this additional criterion, we conclude that Patricia in this fragment is not contingent, mostly because she has not gathered any information on the students’ understanding. Because the teacher did not perform any diagnostic strategies, it is impossible to know whether the teacher had adapted her teaching method to suit the students’ understanding. The performance of diagnostic strategies is thus a necessary precondition for scaffolding. As we will see in the next example fragment, however, the performance of diagnostic strategies alone is not necessarily a sufficient condition for scaffolding.

Example fragment, John: Nonscaffolding with diagnostic strategies

In the lesson from which this example fragment stems, the teacher (John) moved around the classroom and talked with the groups to provide support for the students when needed. The group of (four) students that was supported in this example fragment had been working for about five minutes on the assignment before the teacher arrived. In these five minutes, the students did not perform the first step of the assignment (checking whether the concepts are understood), but rather immediately began with the second step (choosing three concepts that are related). The transcript of the ensuing teacher – small-group interaction is provided below.

Example fragment, John1 Teacher Are there any concepts that you didn’t fully understand?

[step 1: diagnostic strategy]2 Student 1 Well, the descriptions are there, so...3 Teacher But do you understand those descriptions? That used to happen

to me when I was young, that I didn’t get the descriptions. [step 1: diagnostic strategy]

4 Student 2 You mean, what it really means?5 Teacher Yes6 Student 2 Yes, I get that7 Teacher Yes? You too? Yes? You too?8 Student 3 Hm. (nods yes)9 Teacher For example, I just explained the concept of internal market to

another group. Does that sound familiar? [step 1: diagnostic strategy]

10 Student 1 Well, actually, no11 Teacher No, you see, I told you so.12 Student 3 Yes, but we read this very quickly

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13 Teacher Yes, but now it is about reading thoroughly so that you know what you are talking about. Taking the word “internal market” as an example. I just explained that to them (other group). Imagine the EU- how many countries does the EU have? [step 3: Intervention]

14 Student 4 Twenty-seven15 Teacher You make wooden shoes in the Netherlands. You can easily sell them to her (refer-

ring to another student in the group) in that other country [step 3: intervention strategy]

16 Student 3 Yes17 Teacher No borders, nothing. You make stuff, you can sell it everywhere. This is your inter-

nal market. So, in the European countries, you can sell whatever you want to each other. Nobody says you can’t. Before one had to? [step 3: intervention strategy]

18 Student 4 Something with taxes19 Teacher Before you had to pay taxes when crossing the border. Yes! Paying import taxes.

Well, that’s the EU. It’s an advantage because it saves you money, of course. Ok, please continue [step 3: intervention strategy]

20 (students continue working)21 Teacher (walks away)

As soon as the teacher left, student 3 uttered, “I still don’t get it!” and the students went on with what they had been doing. Later on, the students were using the concept of internal market in a series (internal market – import – import taxes). Their choice of series might seem to suggest that they understood, to a certain extent, the meaning of internal market. However, they did not discuss why these concepts were related, and they demonstrated misunderstandings of the concept of internal market (“internal market means that you send to other people” or “internal market is what he just said, paying taxes”).

If we approach this interaction fragment using the model of contingent teaching, we see that John performed the first step of contingent teaching (using diagnostic strategies) by asking questions such as “Do you understand those descriptions?” (line 3) and “Does that sound familiar?” (line 9). However, these diagnostic questions are yes/no questions and thus elicit claims of understanding, such as “Yes, I get that” (line 6) and of nonunderstanding, such as “Well, actually, no” (line 10). John does not seem to accept the claims of understanding; he keeps asking diagnostic questions. Once he receives a claim of nonunderstanding (line 10), however, he decides to start helping the students. Yet he still does not have enough information about their actual understanding; he only knows that the students claim to not understand the concept of internal market. He does not know what the students may already know about the concept or how they understand the concept.

John skipped step 2 of the model of contingent teaching, checking the diagnosis, and after hearing the claim of nonunderstanding, he started supporting the students (line 13; step 3 of the model of contingent teaching). However, without information

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on the students’ understanding, John lacked a basis to be contingent upon. We can see that when he was helping the students, he was quite directive and provided an explanation of the concept without adequately involving the students or making them think actively. In the end, he appeared to assume that the students understood the concept of internal market as he walked away. He did not perform step 4 of the model of contingent teaching, checking the students’ learning. Although he did transfer the responsibility for the task back to the students by walking away (line 23), we cannot be sure whether this was appropriate. Of all the steps in the model of contingent teaching, he mainly focused on the step of helping students (step 3), and the help that he provided was directive. He was unable to access the students’ understanding. He did not gather information on the students’ actual understanding and did not help the students with exactly those concepts that they did not understand (as he never ascertained their actual understanding). Therefore, we argue that this example fragment represents a nonscaffolding interaction.

Example fragment, Ben: Scaffolding

The teacher-student interaction in Ben’s example fragment begins with a similar situation to that depicted in the previous example: The students, working in a group of six, claimed that they had checked the meanings of all of the concepts, and the teacher asked them about internal market (this was one of the most important concepts of the project). The students had been working for about 15 minutes when they asked for help. While working, they did not check the meanings of all of the concepts (step 1 of the assignment), but immediately began to formulate several series of related concepts (step 2 of the assignment), such as export – import – internal market and rights – peace – freedom. The transcript of Ben’s example fragment is presented below.

Example fragment, Ben1 Teacher Have you checked that? (all concepts) [step 1: diagnostic strategy]2 Student 5 Yes3 Student 3 Yes4 Teacher So you get all the concepts? [step 1: diagnostic strategy]5 Student 3 Eh, yes, almost6 Teacher Student 2, what is internal market? [step 1: diagnostic strategy]7 Student 2 Not by heart8 Teacher Well, you don’t have to, but what comes to your mind? [step 1: diagnostic strategy]9 Student 2 Well, the market10 Teacher Trade? [step 2: checking the diagnosis]

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11 Student 2 Goods12 Teacher And then, are they standing somewhere, sitting, hanging? What happens to them?

[step 3: intervention strategy]13 Student 3 International14 Student 5 (reads from the book) “Free traffic of people, goods and services”15 Teacher The beginning was very good, and, I think, because you said it starts with people,

goods and services and then? Then I don’t understand anymore [step 3: intervention strategy]

16 Student 6 That they can cross the borders freely17 Teacher Oh, well, what did student 6 say [step 3: intervention strategy]18 Student 3 I don’t know19 Teacher Well, again, because it was interesting [step 3: intervention strategy]20 Student 6 That they can cross the border freely. No customs, no toll and everything21 Teacher Is that a good second sentence, student 2? That they can cross the border freely?

[step 3: intervention strategy]22 Student 2 Yes23 Teacher Do you agree? (Addresses student 2) [step 3: intervention strategy]24 Student 2 Yes (laughs)25 Teacher Well, then, we made a whole sentence, so the thing with goods, tell me, what is the

sentence? (Addresses student 2) [step 4: checking students’ learning]26 Student 2 Eh, free trade, people27 Student 5 Goods28 Student 2 Stuff, also across the border29 Teacher Also across the border, did he say that? What did he say? Student 6, again

[step 3: intervention strategy]30 Student 6 Free to cross the border31 Teacher Ok, free to cross the border. And what does 6 means by that, student 4?

[step 4: checking students’ learning]32 Student 4 That you don’t have to pay and stuff33 Teacher That you don’t have to pay and? [step 3: intervention strategy]34 Student 3 To wait at the customs, you don’t have to line up35 Teacher Great. Student 2, one more time [step 4: checking students’ learning]36 Student 2 Rules37 Teacher Yes, that there are fewer rules to cross the customs is a good idea, if I may. But now,

the whole sentence [step 4: checking students’ learning]38 Student 2 [...] Free trade of people, goods and services across the border39 Teacher Ok, and in what area? (addressing student 2) [step 3: intervention strategy]40 Student 5 EU41 Student 2 EU? 42 Teacher Yes. If you agree, then you can repeat what he said. Well, I feel you have mastered

this concept. Could you now make a series using it? Or was that not your plan? 43 Student 3 We had two other series44 Teacher Ok, can you continue with the assignment now?

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45 Student 3 Yes46 Student 5 Yes47 Teacher Ok. And if there are any concepts you don’t get, try to clarify it first because otherwise

it’s hard to use them, ok?48 Teacher (walks away)

After the teacher left, the students used the concept of internal market and demonstrated their understanding of the concept (e.g., “There are no customs anymore in the EU; it’s actually one big country”). If we approach this fragment using the model of contingent teaching, we see that the teacher began by diagnosing the students’ understanding (step 1 of contingent teaching) by asking: “Student 2, what is internal market?” (line 6) and “Well, you don’t have to, but what comes to your mind?” (line 8). The teacher did not accept the students’ claim of not understanding (“Not by heart” line 7), as John did, but rather made the students think actively and elicited demonstrations of understanding. In line 10, Ben checks his diagnosis because the concept of market can be interpreted in several ways. In line 12, he starts helping (step 3), and he obviously reduces the degrees of freedom for the students, as he prompts them while making use of their knowledge. He helped in an interactive and activating way, providing precisely the degree of control that was needed. In the end, he transferred the responsibility for the task back to the students; he asked them to explain the concept again in their own words (step 4; checking students’ learning; for example, see lines 35 and 37). The students’ demonstrations of understanding prove that Ben successfully transferred back the responsibility for the task. We consider this fragment to be a good example of scaffolding because Ben focused on the students’ understanding and made sure that he could transfer the responsibility back to the students. He gathered information about the students’ understanding and helped them with exactly those areas that they did not grasp.

Summary

In this portion of the study, we sought to answer our first research question: How can the model of contingent teaching be applied to measure contingency in teacher – small-group interactions? The model of contingent teaching enabled us to analyse the scaffolding process on a general level; it enabled us to distinguish between different phases of contingent teaching. Patricia, for example, did not perform any diagnostic strategies (step 1). Both John and Ben used diagnostic strategies (step 1). However, only Ben succeeded in revealing information about the students’ actual understanding. We also saw that the second step of the model of contingent teaching, checking the

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diagnosis, was rarely used; Ben used this step once. Furthermore, all three teachers supported their students with intervention strategies (step 3). Finally, only Ben used the fourth step of the model of contingent teaching, checking students’ learning. This model of contingent teaching provides us with insight into the phases that a teacher passes through with his or her students while scaffolding. Diagnostic strategies play a crucial role in this model; the performance of diagnostic strategies appears to be a necessary but insufficient condition for scaffolding. John, for example, utilised diagnostic strategies; he tried to find out more about the students’ understanding. However, he was not using information about the students’ understanding for the simple reason that he did not succeed in gathering this information. He stopped diagnosing even though he had only received claims of (not) understanding. The model of contingent teaching, thus, provides us with general insight into the phases of scaffolding. With the additional criterion (the teacher helps students to understand precisely those concepts that they do not grasp and gathers information about their level of understanding), we can even, on a broad level, decide upon contingency in a particular interaction fragment. However, the model of contingent teaching does not reveal whether a teacher is truly adapting the level of control that he or she exerts to the students’ understanding. Therefore, we will now use the contingent shift framework to analyse the entire corpus of fragments, including the three example fragments.

Characterising Scaffolding with the Contingent Shift Framework

Contingent shift framework: Entire corpus

In this section, we will first explore whether the contingent shift framework is effective in revealing variability with regard to contingency in different fragments (research question 2) for the entire corpus. The means and standard deviations of the variables are provided in Table 6.

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Table 6Means and Standard Deviations of Contingency, Degree of Control, Students’ Understanding, and Student Mode

M (SD)Contingency (0/1) 0.76 (0.43)Degree of control (0-5) 2.19 (1.5)Students’ understanding (0-2) 1.06 (0.82)Student mode of expression (0-2) 1.33 (0.76)

Note. Contingency: 0=not contingent, 1=contingent; Teacher degree of control (TDc): TDc0=no control; TDc1=lowest control, TDc2=low control, TDc3=medium control, TDc4=high control, TDc5=highest control; Students’ understanding (SU): SU0=poor understanding, SU1=partial understanding, SU2=good understanding; Student mode of expression (SM): 0=claim, 1=demonstration minimal, 2=demonstration extensive.

All of the variables demonstrated a high degree of variability, indicating that the coding schemes are able to distinguish between different levels. As for contingency, we can see that the mean is fairly high, indicating that the teachers were quite contingent. This was probably due to the fact that about half of the teachers were trained in scaffolding. When we examine the means per condition, we indeed see that the mean was 0.44 (0.50) in the nonscaffolding condition and 0.85 (0.36) in the scaffolding condition.

Contingent shift framework: Three example fragments

The same three interaction fragments that were used in the qualitative analysis will now be analysed using the contingent shift framework to explore research question 2 (How can the contingent shift framework be applied to measure contingency in teacher – small-group interactions?).

Example fragment, Patricia: Nonscaffolding without diagnostic strategies

Table 7 presents the coded example for Patricia. The turns of each participant are presented in a separate column to visually depict the flows of understanding and reasoning between the different students and the teacher (in this case, only one student is participating in the conversation). All teacher turns were coded according to the degree of control exerted by the teacher. All student turns were coded according to their understanding and mode of expression. Finally, following the rules of contingency, each three-turn sequence (consisting of a teacher turn, a student turn, and a teacher turn) was coded as contingent (C) or not contingent (NC).

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In this short interaction fragment, the student provides a few brief responses. The interaction fragment contains three three-turn sequences. The first three-turn sequence (lines 1-3) is noncontingent. The teacher jumps from exerting no control at all to exerting the highest level of control (she is providing the answer). Although the answer provided by the student (line 4) was considered correct by the teacher, we coded this as no understanding can be determined because the teacher had already pointed to the right answer and the student was merely reading this aloud from the booklet. However, the contingent step that, according to the model, should follow this behaviour (SUX) is to elicit a demonstration (see Appendix H for the additional rules). The teacher follows these guidelines, and the second three-turn sequence (lines 3-5) is therefore coded as contingent. The last three-turn sequence (lines 5-7) is considered noncontingent because the student gave no extensive demonstration.

Overall, this interaction fragment is noncontingent for the most part, according to the contingent shift framework. The qualitative analyses using the model of contingent teaching demonstrated that Patricia was not performing any diagnostic strategies, and this probably accounts for the noncontingency of this interaction fragment. However, the second three-turn sequence was contingent. While helping a student, a teacher can also obtain information regarding a student’s understanding. This information can enhance contingency. However, performing diagnostic strategies first probably provides a more detailed and nuanced picture of a student’s understanding.

Example fragment, John: Nonscaffolding with diagnostic strategies

Table 8 presents the coded transcript of the example fragment for John. In this fragment, all of the students are, to some extent, contributing to the conversation. However, the students mostly provide short claims of understanding as opposed to demonstrations. Furthermore, the teacher jumps from student to student, and there are no two successive three-turn sequences with the same student; every three-turn sequence involves a new student. In the three-turn sequence in lines 15-17, for example, student 3 responds, whereas in the subsequent three-turn sequence (lines 17-19) student 1 responds. Therefore, we cannot conclude that the teacher’s instruction is contingent or noncontingent upon one particular student’s needs. We could say that the teacher is treating the group of students as a single entity and directing his contingent or noncontingent instruction towards the group (as opposed to a single student).

If we compare the qualitative and quantitative analyses of this fragment, we reach a similar, though more nuanced, conclusion regarding the teacher’s contingency. Two out of the nine three-turn sequences were considered contingent here (22.2%). This indicates that this fragment is noncontingent, at least for the most part. In the

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Chapter 4

Tabl

e 7

Exam

ple

Frag

men

t, Pa

trici

a, C

oded

Teac

her

Stud

ent

(S)1

S2S3

S4TD

cSU

SMC

/NC

Rem

arks

1(te

ache

r not

ther

e ye

t)0

2M

iss,

look

“whe

n it’s

up

to o

ne p

erso

n” a

nd h

ere

“mor

e ci

tizen

s”X

1N

CTe

ache

r doe

s no

t elic

it a

dem

onst

r.

3

Yes,

so

you

need

one

mor

e co

ncep

t. Yo

u al

read

y ha

ve tw

o co

ncep

ts, d

emoc

racy

and

di

ctat

orsh

ip. W

hich

one

cou

ld g

o w

ith th

ese?

Be

caus

e th

ese

do n

ot g

o to

geth

er, i

n th

e en

d yo

u ha

ve to

find

one

mor

e co

ncep

t tha

t fit

s w

ith o

ne o

f you

rs. F

or e

xam

ple,

this

one

(p

oint

s in

the

book

let).

5

4“h

uman

righ

ts” (

read

s fro

m th

e bo

okle

t)X

1C

Elic

its

dem

onst

r.

5Ye

s, a

nd d

oes

that

go

with

dic

tato

rshi

p or

with

, eh

, dem

ocra

cy?

3

6eh

, dem

ocra

cy2

1N

CN

o de

mon

str.

7Ye

s, s

o no

w y

ou h

ave

thre

e co

ncep

ts a

nd o

ne

does

not

bel

ong

(wal

ks a

way

). 0

Not

e. T

Dc=

teac

her d

egre

e of

con

trol (

TDcN

OC

=not

on

cont

ent,

TDc0

=no

cont

rol,

TDc

1=lo

wes

t con

trol,

TDc

2=lo

w c

ontro

l, TD

c 3=

med

ium

con

trol,

TDc

4=hi

gh

cont

rol,

TDc

5=hi

ghes

t con

trol);

SU

=Stu

dent

’s un

ders

tand

ing

(SU

NO

C=n

ot o

n co

nten

t, SU

X=no

und

erst

andi

ng c

an b

e de

term

ined

, SU

0=po

or u

nder

stan

ding

, SU

1=pa

rtial

und

erst

andi

ng, S

U2=

good

und

erst

andi

ng);

SM=S

tude

nt m

ode

of e

xpre

ssio

n (S

MN

OC

=not

on

cont

ent,

SM0=

clai

m, S

M1=

dem

onst

ratio

n m

inim

al,

SM2=

dem

onst

ratio

n ex

tens

ive)

, C=C

ontin

genc

y (C

=con

tinge

nt, N

C=n

ot c

ontin

gent

).

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qualitative analysis, we pointed out that John initially did not take the students’ claims of understanding for granted. He kept asking questions until the students acknowledged that they did not understand. However, his questions all required only a yes/no answer, as opposed to a demonstration. This indicates that these three-turn sequences were noncontingent. In helping the students, he did not decrease the level of control that he was exerting when students were demonstrating their understanding. As a result, when he finally did decrease the level of control that he was exerting by walking away, he did not know if the students understood the concept.

Example fragment, Ben: Scaffolding

Table 9 presents the coded transcript of the example fragment for Ben. As the table shows, students 2, 3, 5 and 6 are the main contributors to the conversation. The teacher focused primarily on student 2 but also acknowledged and used the contributions of the other students.

If we were to ignore which student said what, the contingency percentage for this fragment for the whole group would be 98% (19 out of 20 three-turn sequences were contingent). However, if two or more three-turn sequences included responses from the same student, we can conclude that the teacher is mainly being contingent towards that particular student because we do not have any information regarding the understanding of the students who did not provide any responses.

When we use the three-turn sequence consisting of lines 6-8 as an example for analysis, we see that the teacher’s turn (line 6) was based on student 3’s response (line 5), in which he stated hesitantly that he understood almost all of the concepts. The teacher seemed to take this as information indicating that the group of students possessed at least partial understanding; in line 6, he asked another student (student 2) to explain the meaning of the term “internal market”. We were not able to conclude that the turns of the teacher in this three-turn sequence (lines 6-8) were particularly contingent on the responses of student 2; although student 2 participated in the exchange, the teacher also used information of other group members. However, in the three-turn sequence consisting of lines 8-10, we could say that the teacher’s responses were particularly contingent upon the understanding demonstrated by student 2 because the teacher adapted the level of control he exerted in response to the answers given by student 2 in the previous three-turn sequence. Therefore, we added a 2 (for student 2) in brackets behind the C for contingency (as opposed to a g for group). In examining the contingency scores for the three-turn sequences, we determined that 5 out of the 19 contingent three-turn sequences were contingent upon the responses of student 2 (26%). The other 14 contingent three-turn sequences can be considered

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Chapter 4

Tabl

e 8

Exam

ple

Frag

men

t, Jo

hn, C

oded

Teac

her

S1S2

S3S4

TDc

SUSM

C/N

CR

emar

ks

1Ar

e th

ere

any

conc

epts

that

you

di

dn’t

fully

und

erst

and?

1D

isco

vers

un

ders

tand

ing

2W

ell,

the

desc

riptio

ns

are

ther

e so

20

NC

(g*)

3Bu

t do

you

get t

hose

des

crip

tions

? Th

is u

sed

to h

appe

n to

me

whe

n I w

as y

oung

, tha

t I d

idn’

t get

the

desc

riptio

ns.

3El

icits

no

dem

onst

r.

4W

hat i

t rea

lly

mea

ns, y

ou

mea

n?N

OC

5Ye

s.N

OC

6Ye

s, I

get i

t.2

0N

C(g

)

7Ye

s? Y

ou to

o? (A

ddre

sses

stu

dent

3)

3El

icits

no

dem

onst

r.

8H

m (n

ods

yes)

20

NC

(g)

9Fo

r exa

mpl

e, I

just

exp

lain

ed th

e co

ncep

t of i

nter

nal m

arke

t to

anot

her

grou

p. D

oes

that

sou

nd fa

milia

r?

3El

icits

no

dem

onst

r.

10W

ell,

actu

ally,

no

00

C(g

)

11N

o, y

ou s

ee, I

told

you

so.

NO

C

12Ye

s, b

ut w

e re

ad th

is v

ery

quic

kly

NO

C

111


13

Yes,

but

now

you

sho

uld

read

thor

-ou

ghly

so

that

you

kno

w w

hat y

ou

are

talk

ing

abou

t. Ta

ke th

e ph

rase

“in

tern

al m

arke

t” as

an

exam

ple-

I ju

st e

xpla

ined

that

to th

em (o

ther

gr

oup)

. Im

agin

e th

e EU

- how

man

y co

untri

es d

oes

the

EU h

ave?

3El

icits

de

mon

str.

14Tw

enty

-sev

en2

1N

C(g

)

15Tw

enty

-sev

en. I

mag

ine

that

this

is

the

EU. C

ount

ry 1

, 2, 3

, and

4 (p

oint

s at

eac

h st

uden

t’s d

esk)

. Tw

enty

-sev

-en

cou

ntrie

s. Y

ou h

ave

a co

mpa

ny.

5Sh

ould

de

crea

se

cont

rol

16Ye

sX

NC

(g)

17Yo

u m

ake

woo

den

shoe

s in

the

Net

herla

nds.

(Ref

errin

g to

ano

ther

st

uden

t in

the

grou

p). Y

ou c

an e

asily

se

ll th

em to

her

in th

at c

ount

ry.

5El

icits

no

dem

onst

r.

18Ye

sX

C(g

)

20So

met

hing

w

ith ta

xes

21

NC

(g)

21

Befo

re y

ou h

ad to

pay

taxe

s w

hen

cros

sing

the

bord

er. T

here

you

go,

pa

ying

impo

rt ta

xes.

Wel

l, th

at’s

the

EU. I

t’s a

n ad

vant

age

beca

use

it sa

ves

you

mon

ey, o

f cou

rse.

Ok,

co

ntin

ue p

leas

e.

5Sh

ould

de

crea

se

cont

rol

22(s

tude

nts

con-

tinue

wor

king

)X

23(w

alks

aw

ay)

0N

C(g

)

Not

e. TDc=

teac

her d

egre

e of

con

trol (

TDcN

OC

=not

on

cont

ent,

TDc0

=no

cont

rol,

TDc

1=lo

wes

t con

trol,

TDc

2=lo

w c

ontro

l, TD

c 3=

med

ium

con

trol,

TDc

4=hi

gh

cont

rol,

TDc

5=hi

ghes

t con

trol);

SU

=Stu

dent

’s un

ders

tand

ing

(SU

NO

C=n

ot o

n co

nten

t, SU

X=no

und

erst

andi

ng c

an b

e de

term

ined

, SU

0=po

or u

nder

stan

ding

, SU

1=pa

rtial

und

erst

andi

ng, S

U2=

good

und

erst

andi

ng); SM

=Stu

dent

mod

e of

exp

ress

ion

(SM

NO

C=n

ot o

n co

nten

t, SM

0=cl

aim

, SM

1=de

mon

stra

tion

min

imal

, SM

2=de

mon

stra

tion

exte

nsiv

e); C

=Con

tinge

ncy

(C=c

ontin

gent

, NC

=not

con

tinge

nt).

* Con

tinge

nt fo

r the

gro

up o

f stu

dent

s

112

Chapter 4

Tabl

e 9

Exam

ple

Frag

men

t, Be

n, C

oded

Teac

her

S1S2

S3S4

S5S6

TDc

SUSM

C/N

C

Rem

arks

1H

ave

you

chec

ked

that

? (a

ll th

e co

ncep

ts)

NO

CD

oes

not

refe

r to

unde

r-st

andi

ng2

Yes

NO

C3

Yes

NO

C

4So

you

get

all

the

conc

epts

? 1

Ref

ers

to

unde

r-st

andi

ng

5Eh

, yes

, al

mos

t1

0C

(g*)

6St

uden

t 2, w

hat i

s in

tern

al

mar

ket?

1

7N

ot b

y he

art

00

C(g

)

8W

ell,

you

don’

t hav

e to

, but

wha

t co

mes

to y

our m

ind?

1

Asks

for

dem

onst

r.

9W

ell,

the

mar

ket

02

C(2

**)

10Tr

ade?

4

Teac

her

adds

new

in

fo b

ut

does

not

gi

ve th

e an

swer

11G

oods

22

C(2

)

12An

d, th

en, a

re th

ey s

tand

ing

som

ewhe

re, s

ittin

g, h

angi

ng?

Wha

t hap

pens

to th

em?

2As

ks fo

r de

mon

str.

13In

tern

atio

nal

02

C(g

)

113


14

(read

s fro

m th

e bo

ok)

“Fre

e tra

ffic

of

peop

le,

good

s an

d se

rvic

es.”

XC

(g)

15

The

begi

nnin

g w

as v

ery

good

an

d, I

thin

k, b

ecau

se y

ou s

aid

it st

arts

with

peo

ple,

goo

ds a

nd

serv

ices

, and

then

? Th

en I

don’

t un

ders

tand

it a

nym

ore

2

Leve

l 2

with

fe

edba

ck;

Asks

for

dem

on-

stra

tion

16

That

th

ey c

an

cros

s th

e bo

rder

s fre

ely

22

C(g

)

17O

, wel

l, w

hat d

id s

tude

nt 6

say

? 2

No

feed

back

18I d

on’t

know

00

C(g

)

19W

ell,

agai

n, b

ecau

se it

was

in

tere

stin

g2

Asks

for

dem

onst

r.

20

That

they

ca

n cr

oss

the

bord

er

freel

y. N

o cu

stom

s,

no to

ll an

d ev

eryt

hing

12

C(g

)

21Is

that

a g

ood

seco

nd s

tate

men

t, st

uden

t 2?

That

they

can

cro

ss

the

bord

er fr

eely

? 3

22

Yes

20

NC

(g)

23D

o yo

u ag

ree?

(Add

ress

es

stud

ent 2

)3

114

Chapter 4

Teac

her

S1S2

S3S4

S5S6

TDc

SUSM

C/N

CR

emar

ks

24

Yes

(laug

hs)

20

C(2

)

25W

ell,

then

we

mad

e a

who

le

sent

ence

....s

o th

e th

ing

with

go

ods,

tell

me,

wha

t is

the

sent

ence

? (A

ddre

sses

S2)

1

26Eh

, fre

e tra

de,

peop

le0

2C

(2)

Asks

for

dem

onst

r.

27G

oods

11

C(g

)

28St

uff,

also

ac

ross

the

bord

er0

2C

(g)

Asks

for

dem

onst

r.

29Al

so a

cros

s th

e bo

rder

, did

he

say

that

? W

hat d

id h

e sa

y? S

tude

nt

6, a

gain

2As

ks fo

r de

mon

str.

30Fr

ee to

cr

oss

the

bord

er2

2C

(g)

31O

k, fr

ee to

cro

ss th

e bo

rder

. An

d w

hat d

oes

6 m

eans

by

that

, st

uden

t 4?

1As

ks fo

r de

mon

str.

32Th

at y

ou

don’

t hav

e to

pay

and

st

uff

22

C(g

)

33Th

at y

ou d

on’t

have

to p

ay. a

nd?

1

34

To w

ait a

t th

e cu

stom

s,

you

don’

t ha

ve to

line

up

22

C(g

)

35G

reat

. Stu

dent

2, o

ne m

ore

time

1C

heck

s st

uden

t’s

unde

rst.

36R

ules

12

C(g

)

115


37Ye

s, th

at th

ere

are

few

er ru

les

for

cros

sing

cus

tom

s is

a g

ood

idea

, if

I may

… B

ut n

ow, t

he w

hole

se

nten

ce.

4

38

Free

trad

e of

peo

ple,

go

ods

and

serv

ices

fre

e ac

ross

th

e bo

rder

12

C(2

)

39O

k, a

nd in

wha

t are

a? (A

ddre

sses

S2

)4

40EU

21

41EU

?2

1

42

Yes,

if y

ou a

gree

, the

n yo

u ca

n re

peat

wha

t he

said

. Wel

l, I f

eel

you

have

mas

tere

d th

is c

once

pt.

Can

you

mak

e a

serie

s w

ith it

no

w?

Or w

as th

at n

ot y

our p

lan?

NO

C

43W

e ha

d tw

o ot

her s

erie

sN

OC

44O

k, c

an y

ou c

ontin

ue w

ith th

e as

sign

men

t now

? N

OC

45Ye

sN

OC

46Ye

sN

OC

47O

k, a

nd if

ther

e ar

e an

y co

ncep

ts

you

don’

t get

, try

to c

larif

y th

em

first

bec

ause

oth

erw

ise

it’s h

ard

to

use

them

, ok?

N

OC

48(w

alks

aw

ay)

0C

(g)

Not

e. TDc=

teac

her d

egre

e of

con

trol (

TDcN

OC

=not

on

cont

ent,

TDc0

=no

cont

rol,

TDc

1=lo

wes

t con

trol,

TDc

2=lo

w c

ontro

l, TD

c 3=

med

ium

con

trol,

TDc

4=hi

gh

cont

rol,

TDc

5=hi

ghes

t con

trol);

SU

=Stu

dent

’s un

ders

tand

ing

(SU

NO

C=n

ot o

n co

nten

t, SU

X=no

und

erst

andi

ng c

an b

e de

term

ined

, SU

0=po

or u

nder

stan

ding

, SU

1=pa

rtial

und

erst

andi

ng, S

U2=

good

und

erst

andi

ng); SM

=Stu

dent

mod

e of

exp

ress

ion

(SM

NO

C=n

ot o

n co

nten

t, SM

0=cl

aim

, SM

1=de

mon

stra

tion

min

imal

, SM

2=de

mon

stra

tion

exte

nsiv

e); C

=Con

tinge

ncy

(C=c

ontin

gent

, NC

=not

con

tinge

nt).

* Con

tinge

nt fo

r the

gro

up o

f stu

dent

s**

Con

tinge

nt fo

r stu

dent

2

116

Chapter 4

contingent upon the understanding demonstrated by the group, or at least by more than one group member (74%).

Using the contingent shift framework, we see that the teacher’s behaviour in this fragment appears to be highly contingent upon the understanding demonstrated by the students. This corresponds with the outcomes of our qualitative analyses using the model of contingent teaching. Ben used all four steps of contingent teaching, and his actions were highly contingent upon the students’ needs, especially the needs of student 2.

Summary

In this section, we sought to answer our second research question: How can the contingent shift framework be applied to measure contingency in teacher – small group interactions? The three teachers in the example fragments displayed quite different degrees of contingency. Patricia was relatively directive in her support, although she was able to adapt her level of control in one three-turn sequence. Both John and Ben used diagnostic strategies. However, the contingent shift framework demonstrated the differences in their use of contingency. The diagnostic strategies employed by Ben were coded as questions exerting the lowest level of control. His questions were very open, contained no new information and elicited demonstrations from the students. The diagnostic strategies employed by John, however, were coded as questions exerting a medium degree of control; although they added no new information, his questions did not elicit demonstrations of understanding from the students. Because of this, the first part of John’s interaction fragment was determined to be noncontingent. When providing support, Ben was better able to adapt his level of control to the students’ understanding because he had more information about their understanding. Ben and his students are co-reasoning, whereas John himself is doing most of the reasoning in his interaction fragment. In providing support, John does not follow the contingency rules, such as decreasing the level of control when students are giving correct answers or increasing the level of control when students are giving incorrect answers. When Ben walks away, he knows that the students understand the concept of internal market; in contrast, when John walks away, he does not know how the students understood this concept in the first place and whether they now, after his support, understand the concept.

The contingency framework thus enables detailed analyses of the ways in which teachers adapted their level of control to suit the students’ understanding. In addition, we were even able to determine whether the teachers were contingent upon one particular student’s understanding or on the understanding demonstrated by the group

117


as a whole. When the teacher does not merely accept students’ claims but rather elicits their demonstrations, this behaviour plays an important role in the contingent shift framework and this relates to the prominent role played by diagnostic strategies (step 1) in the model of contingent teaching. This micro-level analysis enhances the more qualitative analysis with the model of contingent teaching, which enables us to more precisely determine the degree to which a teacher adapts his or her exertion of control to the students’ understanding. This type of adaptation lies at the core of the concept of scaffolding, i.e., contingency.

DISCUSSION

In this study, we sought to contribute to classroom scaffolding research by developing instruments for systematic analysis of scaffolding from an interactive perspective combining general and micro-level analyses. We have argued that such an interactive contingency approach to scaffolding is essential to reach a genuine understanding of the scaffolding process.

In this chapter, we sought to answer our main research question: How can classroom scaffolding in teacher – small-group interactions be analysed from a contingency perspective that takes the interactive nature of scaffolding into account? The model of contingent teaching proved useful in generating a general, qualitative impression of the different phases of contingent teaching; our analysis revealed different patterns for different interactions. The contingent shift framework proved suitable for analysing scaffolding interactions at a micro-level as it demonstrated variability in the larger corpus of data and provided us with more detailed information on the teachers’ usage of contingency, or scaffolding. Such a micro-level analysis seems necessary to reveal whether a teacher is truly adapting his or her degree of control to suit the students’ levels of understanding. Building upon the studies of Nathan and Kim (2009) and Pino-Pasternak et al. (2010), we demonstrated that the contingent shift framework can be used to analyse teacher – small-group interactions in less structured tasks. Furthermore, we demonstrated how the dynamics between a teacher and different group members can be explored using this framework. Previously, the contingent shift framework was only used to analyse one-to-one interactions, but we demonstrated that it can also be used to analyse teacher – small-group interactions. The contingent shift framework enables analysis of the interactions both between the teacher and a small group of students and between the teacher and individual group members. By no means are we suggesting that either scaffolding the group or scaffolding a particular student in the group is a better approach. We intended to make clear that this distinction

118

Chapter 4

can be made using the contingent shift framework. We sought to contribute to the current state of research on scaffolding measurement

not only by demonstrating the possibility of distinguishing between students but also by enhancing the distinction between students’ claims and demonstrations. The keys to effective scaffolding are contingent teaching and knowing what to be contingent upon; the teacher therefore needs information about the students’ understanding and thus demonstrations. Moreover, not only do student demonstrations provide the teacher with information, they also stimulate students’ active reasoning; the student is the one who must engage in active reasoning, not the teacher. Scaffolding is about helping only where and when necessary. This means that the student should do as much as possible. By stimulating students’ active reasoning, the responsibility is already, to some extent, transferred to the student. Additionally, the teacher is better able to judge when and where to help and when to transfer the responsibility back to the learner.

Some researchers argue that providing an answer or an explanation (the highest level of teacher control in our coding scheme) cannot, by definition, be considered scaffolding because it is too directive. We hope that we have explained that scaffolding is not defined by the teacher’s degree of control per se, but rather by the contingency upon the students’ needs. Therefore, if a student does not appear to understand a particular concept, he or she might need the teacher to temporarily take over a part of the task (e.g., by providing an explanation or demonstration) to enable the student to move on. The crucial point here is that the support needs to be contingent and should always be aimed at transferring the responsibility for the task back to the student whenever possible.

Limitations

The use of the contingent shift framework is an elaborate endeavour. First, all interaction fragments need to be transcribed. Second, all teacher and student turns need to be coded. Finally, the contingency rules need to be applied. However, we argue that such microanalysis is needed to determine whether a teacher is contingent in his or her interactions with students.

Furthermore, the contingent shift framework focuses strongly on what happens within the interaction fragment itself. Factors such as the nature of previous lessons or a teacher’s preexisting knowledge of a particular student cannot be taken into consideration. However, using complementary information, such as was done when doing the qualitative analyses in this study, might prove useful.

This chapter used the contingent shift framework and the model of contingent teaching to analyse how teachers support student learning within the context of one

119


lesson about the European Union. Learning, however, usually involves long-term processes in which students gradually develop more complex knowledge and skills. An understanding of the role played by scaffolding in such learning processes requires analyses in which students and teachers are closely followed over a longer period of time and in which the two other main features of scaffolding, fading and transfer of responsibility, are included. However, as we stated earlier in this chapter, fading and transfer of responsibility can only be accomplished if performed in a contingent way. Therefore, we have attempted to make a first step in this direction by focusing on the ways in which teachers are contingent upon students’ needs.

Finally, our analysis focused on content-based interactions between teachers and groups of students. Obviously, specific course content is not always the focus of the guidance provided by teachers; support aimed at improving students’ collaborative skills or performance of the task itself is also important. The instruments that we have developed might be used in the future to explore teacher-student interactions in other contexts.

Implications and Future Research

The model of contingent teaching has important implications for practice. As pointed out in the introduction, the use of diagnostic strategies appears to be rare in practice (e.g., Elbers et al., 2008; Lockhorst et al., 2010). An awareness of the different phases of scaffolding could prove highly valuable in guiding teachers’ instructional practices. The model of contingent teaching is a useful instrument for shaping the professional development of teachers. If teachers learn the distinction between the steps, the purposes of the different steps and how the steps can be applied, the use of scaffolding in the classroom will be facilitated and encouraged. Merely applying the steps does not ensure scaffolding, but it is a first and necessary step in learning how to scaffold.

The contingent shift framework appears especially useful for scientific purposes. It enables researchers to compare the interactions between teachers and students and to reach an understanding of the complex process of scaffolding. Hardly any studies have been performed on the effects of scaffolding on student outcomes, such as engagement and achievement. The contingent shift framework can be an important tool in such effect-based research.

Furthermore, the contingent shift framework enables exploration of the influence of contingency on a group as a whole, as opposed to one particular student. One might assume that contingency upon one particular student is most effective for an individual student; however, if contingency upon a group as a whole is equally effective, teachers can work more efficiently.

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